1
$\begingroup$

Suppose that I want to check how good OLS works in some specific environment using Monte Carlo. I can simulate $Y=X\beta+\epsilon$. What should I do in Monte Carlo simulations, do I simulate the whole model on each replication, or do I simulate only $\epsilon$ in each replication, while $X$ is the same across all replications.

$\endgroup$
1
$\begingroup$

Generally you would have some distributional specification for $X$ and re-simulate $X$ on each monte carlo iteration as apposed to using the same $X$ on each iteration. This way the monte carlo simulation would apply to the entire population of $(y,X)$ as apposed to just one finite sample. Also, you have to have some specification for $\epsilon$. Lets say, $\epsilon \sim N(0,\sigma^2)$. Here is how I would do it in R (pseudo code).

b.estimates=matrix(NA,nrow=b,ncol=k) #k is the number of variables 
for(i in 1:b)
{
   #Simulate X here
   e = rnorm(n,0,sd=sigma)
   y= X%*%Beta +e
   b.estimates[i,]=solve(t(X)%*%X)%*%t(X)%*%y  
}  

Hope that helps

$\endgroup$
  • $\begingroup$ Thank you for your answer. I'm asking because I have a problem set, where professor asks to simulate $X$ ones and then to create randomness in Monte Carlo using $\epsilon$, that is in each iteration, only $\epsilon$ and $Y$ are resimulated. I was wondering whether this was just a particular problem, and whether I should do Monte Carlo this way in practice. Drawing $(\epsilon,X)$ in each iteration makes more sense to me as well. $\endgroup$ – Laimond Dec 7 '14 at 10:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.